This paper is a presentation of some useful aspects of a numerical averaging technique that has been applied with considerable success to the orbit prediction problem for artificial satellites. The method has been tested in a variety of situations wherein the satellite is subjected to combinations of perturbations for which adequate analytic theories are practically impossible. The technique provides many of the advantages of analytic averaging while retaining the ability to simulate the effects of any kind of small force that can be deterministically modeled. The theoretical basis for the method is straightforward but the details of its implementation are somewhat confusing and need some explanation. A particularly useful set of averaged equations is presented along with a description of an efficient algorithm for their solution. Examples of the advantages to be obtained by use of the method are included.